One leaf is produced when cos(3θ) starts from the origin then comes back to the origin.
cos(3θ) is zero when θ = 30° = π/6 and θ = 90° = π/2.
dA = ½r2dθ for the infinitesimal area in polar coordinates.
A = ∫½r2dθ from π/6 to π/2.
A = ½·144 ∫cos2(3θ) dθ = 72 ∫[½ + ½cos(6θ)] dθ
A = 72 [θ/2 + (1/12)sin(6θ)] evaluated at π/6 to π/2.
A = 72 [ π/4 + (1/12)sin(3π) - π/12 - (1/12)sin(π)]
A = 72 [π/6] = 12π